Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
826 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 235 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic88 | C2 | semidirect |
| 4. C2×#10622312 | C2 | semidirect |
| 5. #13070887 | C2 | direct (N × H) |
| 6. C2×C11×#346 | C2 | semidirect |
| 17. C2×Dic88 | C22 | semidirect |
| 21. #10622312 | C22 | semidirect |
| 24. C11×#346 | C22 | semidirect |
| 99. C2×#346 | D11 | semidirect |
| 143. #346 | C2×D11 | semidirect |
| 188. C2×C11 | #2251 | semidirect |
| 228. C11 | C2×#2251 | semidirect |
| 268. C2 | #13070887 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic88 | 2 |
| C22×#66864 | 2 |
| C2×#10622309 | 2 |
| C2×#10622312 | 2 |
| #13070887 | 2 |
| C2×C11×#346 | 2 |
| C2×#2251 | 11 |